Parallel approaches to parametric optimization and the convergence of interactive decision support

In the perspective of parallel processing, a new sense of parametric optimization might be promoted. The paper shows that it, is possible to propose new parallel versions of basic optimization algorithms, as well as an advanced method of securing convergence in interactive mnltiobjective optimization and decision support, all based on a modified concept of parametric embedding. This general idea is exemplified for the case of the simplex algorithm of linear programming by a parameterized and coarse-grain parallel augmented simplex algorithm, where a linear optimization problem can be embedded into a multiple-ohjective family which introduces diversified directions of search cutting through the interior of the original admissible set. For the case of nonlinear programming, a parameterized and coarse-grain parallel variable metric pulsar algorithm is shortly presented, where parallel directional searches are combined with a parametrized variable metric to produce a pulsating, robust nonliear programming algorithm. These two examples concern very basic optimization tools ; at the other end of the spectrmn of optimization-related methods, a general method called outranking trials of securing convergence of interactive multiobjective optimization and decision suport is obtained through parameterizing an outranking relation and using basic properties of order-consistent achievement functions in reference point methodology for testing the existence of outranking points by parallel optimization runs. Thus, the paper presents the use of parallel processing to solve a wide range of modified parametric embedding problems related to optimization and decision support.